Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Table of contents

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[11.] PRÆFATIO AD LECTOREM.
Page: 31
[12.] INDEX
Page: 37
[13.] APOLLONII PERGAEI CONICORVM LIB. V. DEFINITIONES. I.
Page: 39 (1)
[14.] II.
Page: 39 (1)
[15.] III.
Page: 39 (1)
[16.] IV.
Page: 39 (1)
[17.] V.
Page: 39 (1)
[18.] VI.
Page: 39 (1)
[19.] VII.
Page: 39 (1)
[20.] VIII.
Page: 39 (1)
[21.] IX.
Page: 40 (2)
[22.] X.
Page: 40 (2)
[23.] XI.
Page: 40 (2)
[24.] XII.
Page: 40 (2)
[25.] XIII.
Page: 40 (2)
[26.] XIV.
Page: 40 (2)
[27.] XV.
Page: 40 (2)
[28.] XIV.
Page: 40 (2)
[29.] NOTÆ.
Page: 41 (3)
[30.] SECTIO PRIMA Continens propoſitiones I. II. & III. Apollonij. PROPOSITIO I.
Page: 43 (5)
[31.] PROPOS. II.
Page: 43 (5)
[32.] PROPOS. III.
Page: 44 (6)
[33.] Notæ in Propoſitionem primam.
Page: 44 (6)
[34.] Notæ in Propoſitionem ſecundam.
Page: 45 (7)
[35.] Notæ in Propoſitionem tertiam.
Page: 45 (7)
[36.] SECTIO SECVNDA Continens propoſitiones IV. V. VI. Apollonij.
Page: 45 (7)
[37.] PROPOSITIO IV.
Page: 46 (8)
[38.] PROPOSITIO V. & VI.
Page: 46 (8)
[39.] Notæ in pro poſitionem quartam.
Page: 47 (9)
[40.] Notæ in propoſitionem quintam.
Page: 48 (10)
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page |< < (43) of 458 > >|
8143Conicor. Lib. V. 58[Figure 58]
Et ſimili modo conſtat, quod breuiſſima egrediens ex puncto L cadit
11f extra S L, & c. Ad vitandam confuſionem figuræ, & prolixitatem demonſtrationis
appoſui duas figuras, in quibus duo caſus ijſdem caracteribus notantur, itaque abſq;
nouo labore, ſi inſpiciatur ſecunda figura, ijſdem verbis prioris caſus, oſtendetur ca-
ſus ſecundus.
Pariter demonſtrabitur, quemadmodum iam oſtenſumeſt, & c. Pars ſecun-
22g da huius propoſitionis innuitur tantummodo pauciſsimis verbis; quare maioris cla-
ritatis gratia integram demonſtrationem hìc afferre libuit.
Demonſtratio ſecundæ partis.
PROPOSITIONIS LI.
Eſto E D æqualis trutinæ H: Dico ex concurſu E vnicum tantùm breui-
ſecantem ramum duci poſſe.
In eadem ſigura, quia ex conſtructione H ad B G eſt, vt G F ad F D, ponitur verò
E D æqualis H; ergo E D ad B G, ſeu D I ad I G (propter ſimilitudinem triangulo-
rum E D I, B G I) eſt, vt G F ad F D, & componendo D G ad G I eſt, vt eadem G D
ad D F; ideoque I G æqualis eſt D F, ſeu A C ſemierecto; igitur B I eſt breuiſsima.
338. huius.
Poſte a ducto quolibet ramo E K ſupra breuiſecantem E B (in prima figura, & in-
fra in ſecunda) occurrente axi in R, & ducta K M perpendiculari ad axim, quæ eum
ſecet in M, & tangentem O B in P. Quoniam (vt dictum eſt) O F ſecatur

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